The present invention relates generally to maintaining a satellite in an orbit, and more particularly to a method of operating a satellite in an earth orbit inclined to a nominal orbit.
It is generally desirable to maintain certain types of satellites, such as communication satellites, in an orbit about the earth so that its location above a specific point on the earth remains fixed. This type of orbit is referred to as a geosynchronous orbit. A geosynchronous orbit enables a communication beam from the satellite to accurately cover a desired area on the surface of the earth. Any deviations from the geosynchronous orbit will alter the coverage of the beam.
To remain in a geosynchronous orbit, the satellite""s nominal orbit is kept substantially within the equatorial plane of the earth. Because of these requirements, the earth""s geosynchronous orbit is crowded with a multitude of satellites. As a result it is necessary to accurately maintain each of the satellites in a corresponding location in the equatorial plane.
A satellite placed in a geosynchronous orbit will experience deviations from orbit due to certain effects such as gravitational forces from the sun and moon, and variations in the gravitational force of the earth due to its oblateness. These forces tend to move the satellite in both a north/south direction, i.e. above or below the equatorial plane, and an east/west direction, i.e., left or right on the orbital path. Excursions in the north/south direction tend to move the satellite out of the equatorial plane and into an inclined orbit. To an observer at a subsatellite location, the satellite appears to move in a xe2x80x9cfigure eightxe2x80x9d pattern once per sidereal day due to the inclined orbit.
It is also possible that the vehicle used to launch the satellite may experience an error resulting in a geosynchronous orbit being reached, but at a non-zero inclined angle as opposed to a zero inclination orbit. The resulting pointing errors from such an event may render a satellite useless unless compensation can be accomplished.
It is usual to describe the attitude in terms of an x, y, z coordinate frame, where z is directed from the satellite to the Earth center, y is directed opposite to the orbit angular velocity, and x completes a right-handed basis (approximately south along a vector normal to the orbit). The x-axis is referred to as the roll axis, the y axis is the pitch axis, and the z axis is the yaw axis.
There are a number of existing schemes for correcting an inclined orbit. It is known to correct an orbit using a pair of identical momentum wheels canted symmetrically away from the pitch axis in a plane containing the pitch axis. It has been taught that roll steering for orbit inclination-induced ground station pointing error corrections are cyclic at orbit frequency.
It has also been taught that a suitable design has an angular momentum vector of the satellite that is steerable with respect to the line of sight of an object being pointed by the satellite (such as the boresight of an antenna), or vice versa, about at least one axis, preferably the roll axis. This is done either by a single axis pointing mechanism (e.g., an antenna pointing mechanism), a single gimbaled momentum wheel, or a combination of fixed wheels. Control signals are generated to steer the angular momentum of the wheel.
Another teaching is that when the orbit inclination with respect to the equatorial plane is nonzero, a single degree of freedom system can operate an ideal satellite to point to the earth center regardless of the direction of the degree of freedom in the x-z satellite plane. For example, if the degree of freedom is along the roll axis, the angular momentum is maintained close to the north/south inertial direction. Similarly, if the degree of freedom is along the yaw axis, the angular momentum is maintained close to the inertial direction normal to the orbit plane.
In U.S. Pat. No. 4,084,772 to Muhlfelder, the angular momentum vector is placed normal to the equatorial plane, and the angular momentum is steerable with respect to the antenna boresight about the roll axis using two fixed wheels. There is a large wheel along the pitch axis, and a small wheel along the yaw axis. An open loop pointing command is introduced in the roll axis. However, this approach is not applicable with active yaw steering since the resulting sinusoidal roll motion is incorrectly coupled back into the yaw axis by way of the yaw estimator.
U.S. Pat. No. 5,100,084 to Agrawal teaches the placement of the momentum vector at a calculated point slightly past orbit normal in order to eliminate roll error. Agrawal also teaches placing the momentum vector in an obit normal/equatorial normal plane and correcting using roll and yaw gimballing means. However, Agrawal does not address the issue of cross-axis coupling.
Additionally, thrusters are typically used to periodically correct the inclination of the orbit by expending fuel, also known as north-south station keeping. North-south station keeping requires a significant amount of the satellite""s propellant. In general, a satellite""s useful life is limited by the station-keeping fuel requirements and the operating life of the satellite can be extended by eliminating the need for north-south station-keeping.
These known methods are either not fully compensating for linear error, not correcting for pointing at points other than earth center, or require either two-axis angular momentum steering, or that the single axis steering be about either the roll or yaw axis. Additionally, these control methods do not address the issue of recovering from a launch failure in which a satellite having active yaw steering reaches a geosynchronous orbit, but has a large inclination angle. Nor do they address the fact that active yaw steering prohibits open-loop pointing command in the roll axis.
It is an object of the present invention to control a satellite in an inclined orbit. It is another object of the present invention to extend the useful life of a satellite. It is yet another object of the present invention to provide a method of recovering from a partial launch vehicle failure.
It is a further object of the present invention to provide a method of modifying the control method used for a satellite already in orbit without making major modifications to the existing control system. It is still a further object of the present invention to align the satellite""s momentum vector normal to the equatorial plane and send open loop sinusoidal roll/yaw pointing commands to the satellite""s attitude control law. It is yet a further object of the present invention to control a satellite with a non-zero inclination angle using a steering law that is designed to operate at a zero inclination angle.
In carrying out the above objects, the present invention provides a method for substantially correcting pointing errors induced by an inclined orbit when using a steering law designed to operate at a zero inclination angle. The control law uses a two axis attitude sensor, such as an earth sensor, to control the spacecraft roll and pitch axes. Yaw axis pointing errors are estimated from observed roll axis activity. This control method presupposes that the orbital plane is aligned with the equatorial plane and maintains the pitch axis perpendicular to the orbit plane through active control of the roll and yaw axes.
Use of such a steering law in an inclined orbit results in a sinusoidal yaw pointing error, relative to the Earth""s equator, with a magnitude equal to the inclination angle. Furthermore, an inclined orbit introduces a sinusoidal roll pointing error, relative to the equator, with a magnitude of approximately 17.8% of the inclination angle. To compensate for the yaw error, the present invention aligns the momentum vector normal to the equatorial plane and open loop sinusoidal yaw pointing commands are sent to the attitude controller. In a similar manner, open loop sinusoidal roll pointing commands are sent to the attitude controller to compensate for the roll error. By using a sinusoidal roll rate command, the present invention avoids the undesired coupling of the roll correction back into the yaw axis.
The present invention may be used to extend the useful life of the satellite, since propellant is not necessarily needed to control orbit inclination. Furthermore, the system and method of the present invention may be used to recover from a partial launch vehicle failure, in which there was insufficient on-board propellant to achieve a desired orbit by altering the control law designed for a zero inclination to control the satellite in an inclined orbit. The present invention may be applied to a satellite already in orbit with minimal effort.
These and other features of the present invention will be better understood with regard to the following description, appended claims, and accompanying drawings.